Could an AI feel emotions?
There is much discussion in philosophy about inner language and the ability to perceive pain (see Pain in philosophy article). Your question is in the area of philosophy and not science. If you define emotion as some state then you can construct simple automata with two states (emotion vs no-emotion). It can be a very complicated state with degrees of truth (percentage of emotion).

Basically, to mimic human emotion you need to make a living human-like organism, and still with todays understanding and technology you will not be able to recognize emotion in it. The only thing you can do is trust when it says "I'm sad". Now we are in the area of the Turing test, which is again philosophy, and not science.